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Vidya Vikasini School (1.C.s.E) Gokhivare, Vasai (E), Dist:Palghar -401 208 II Prelim 2023-2024 Std: X Total Marks: SUBJECT: MATHEMATICS Date: 08/01/2024 hrs Duration: 2 2 80 Answer to this paper must be written on the paper provided separately. You will not be allowed to write during the first 15 minutes. This time is to be spent in reading the Question Paper. The time given at the head of this paper is the time allowed for writing the answers. The intended marks for questionsor parts of questions are given in brackets [ ] All questions from Section A are compulsory. Attempt any 4 questions from Section B SECTION A (Attempt Q.1] Choosethe correct 1. the point P{k,0) value of k is If divides the b) 2 a) 1 2. answersto the all questions from this section) questions from the given options: segmentjoiningthe line c)-2 points A(2,-2) [15] and B(-7,4) in the ratio 1:2, then the d) -1 then the values of x and y are If |3 a) x= 2, y=6 3. The value a) 4. 0 b) x 3 c) 2 Two numbersare in > b) 18, x-12 given a) {1, 2,3,4, -5} 6. If the lines a) 4 7. +3 sin0 cos?9 is d) 1 3:4. If ratio 32 that b) 4 is c) subtracted from each term, then the xE N (-1, 24, 32 ratio becomes 5:7. Find the c) 1/4 c) {1, -2, parallel, 2x 4, then the value of b) (2,3) d) {1, 2,3, 4, 5} k is ordinate is c) (4,3) is: c) {1, 2,3, 4) d) {0,1, 2,3, 4} 6 and B is a point on the x-axis whose abscissa midpoint of AB, the co-ordinates of P are a) (2, 6) is 5} + 4 < 14,x e W b){0, 1, 2,3, 4, 5} whose 3, d) -1/4 inequation point on the y-axis 34 then the solutions set of x = b) -4 d) -24, 2, 3, 4, 5) 2x+ 3y 5 and kx-6y = 7 are The solution set for the a) {1, 2,3, 4, 5} 8. A isa d) x= 3, y=-6 numbers. a) 8, 24 3-2x the x=3, y=-4 c) sin9 + cos8 the expression of b) original 5. = 2, y= -6 d) (3,2) 1 is 4. If P be the The point 9. (0,5) is a) x-axis 10. invariant under b)y-axis reflection the c) The sum of two numbersis 27 and a)12 and 13 b)13 and 14 11. Ina grouped frequency a) median x If A +1 afactor of 3x? is 14. 182. The is 12and 15 the mid-values is 3 26 c) of x and y-axis numbersare: d) 13 and 24 the are used to classes (A):If a wire of length and R Both A d) all then the value of k is 52 cards. The probability 22 cm of the is bent in its the shape of = length of circle of being a redlfac card is the correct explanation is not the correct explanation of A. A d) is true but R Ais false is (A):Two Assertion and R Both A b) Both c) A is d) A is Aand false similar are always triangles 40 cm . two similar congruent. are equal then the triangles is the correct explanation R are true but R is not the correct explanation of A. but R is A. of are true but R true but R formed true. Reason (R):If the areas of a) circle false. is butR then area of a circle, is wire. are true but R c) of the following of these b)Both A and R are true but R a) measurewhich d) 10 selected from a deck of Assertion rnean 6 c) Reason (R):Circumference 15. c) + kx? + 7x + 4, 0 b) card a) product distribution, mode b) a) -1 13. d) both tendency? central 12. in: origin is is triangles are congruent. of A. false. true. Solve the following. Q.2] 1 Solve the quadratic equation 2. Find the value of x' and 'y' x- 3(* + 3) = 0; Give your answercorrect totwo significant figures. (4) (4) if: 7 3 A (2, 5), B (-1, 2) and C 8) are the vertices of a triangle ABC, (5, Find the co-ordinates of M'. Q.3] Hencefind the equation of the 'M line is a point on AB such that AM: MB = 1: passing through the points C and M. 2. (4) Solve the following. 1 Given 2 Draw an inscribing and circle = |1 0| and = A' 9A + ml, of a regular hexagon Find value of m, of side 5.8 2 cm. (4) (4) 3. sOVe the following inequation, write down the solution -2 10x < 13x 10 < 24 10x, x E Z + 94] 1. + set and represent on the it (5) number line: + Solve the following. Aright cylinder inscribed in a sphere circular the shaded region. Give your answer in 10 cm. Find the volume radius of terms of and round it of 2. 10 cm to the nearest tenth. 5cm (3) buys an Aretailer by10% on the at a discount of article paper for are A vertices on the printed price from in GST is 12% and the buyer pays of calculation what would be the question (Take this B (2,2), 2 cm = lunit along C (0,-1) and (2, -2), wholesaler. a He marks the market, he allows a discount of the rate of If GST), predict with the help Use graph 15% printed price but due to competition price to a buyer. 3 real t468.16 for the article up the price 5% on inclusive of the marked tax price of the article. printed both x and y axis). ABCD is a quadrilateral (under (3) whose D(0,1). ABCD on the y-axis and name it as A'B'CD. down the coordinates of A' and B'. Name two points which are invariant under the above reflection. Reflect quadrilateral i) Write ii) i) Name the iv) (4) polygon A'B'CD. Solve the following. K36000 each in buying shares of two companies. Viren buys 15%, 40 shares at a Denis buys 75 shares at a premium of 20%. both receive equal dividends at the Viren and Denis invest discount of 20%,while If A girl fills the be 3. its bucket cylindrical ground and makes a conical radius and its slant 32 cm height Mrs. Khan bought the following Sr. in in articles Find: i)Total Q.6] 1 in of radius with sand. the heap conical She empties the bucket on the is 24 cm. Estimate what would from a (3) departmental store: Rate of 1200 Rs. 600 Rs. Sunflower seeds i) Total 18 cm the height Price Almonds 2. If square root form. Item No. height and heap of the sand. end (3) of the year, find the rate percent of the dividend declared by Denis's company. GST Discount 18 % 12 % Rs. 100 GST paid. bill amount including GST. (4) Solve the following. In a G.P., Common the ratio betweenthe sum of first three terms ratio. and that of the first six terms is 125: 152. Find its (3) 3 2. Virat opened a Savings Bank account ina bank on 16th April 2010. His pass book shows the following entries: Withdrawal Date Particulars Deposit Balance (Rs.) (Rs.) (Rs.) , By cash 2500 2500 April 28th By cheque 3000 5500 May 9th To cheque 2010 April 16, 15th By cash May 24th To cash 1000 5250 4tn To cash 500 4750 30th To cheque 2400 7150 3rd By cash 1800 8950 June July 1600 2010 at 4% per annum 2010? Calculate the interest Virat earned at the end of 31st July, money August, he receive if he closes will the account The horizontai distance betweentwo towers and angle of depression of the bottom tower is 30 and 24 correctly to 6250 May June 3. 4650 850 is What sum interest. of (3) 120m.The angle of elevation of the top first tower as observed from the second Find the height of the respectively. 3 significant of the on 1st two towers. Give your answer figures. (4) E Solve the following. S Samira has a recurring deposit account in a bank of 2000 per month at the rate of 10% p.a. If she gets 83100at the time of maturity, estimate the total time for which the account was held. In ABC the given figure isa triangle and BC is paralll to the y-axis. AB andAC intersectsthe y-axis at P and respectively. i) ii) ii) y Find the length of AB and AC. Find the ratio in which Q Find the equation of the divides line AC. B(-2,3) AC. 3 (3) 2 1 A -1 0 -] -2 C(-2,-4) 4 (3) 12 3 4 Q 3 Ine table shows the of the scores obtained by distribution Brapn sheet and draw an ogive for the shooters on the Y-axis). Scores No. (Take distribution. 160shooters in a shooting competition. Use a 2cm = 10 scores on the X axis and 2cm = 20 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 9 13 20 25 30 22 15 10 8 7 of shooters Use your graph to estimate the following: i) The median. ii) The interquartile (4) range. Q.8] Solve the following. 1 1. Prove that: cos cos 1 + sin 9+ = sec0+ actual length of the diagonal distance AC of the plot The actual area of the plot In (3) a i) The ii) cosec 1 build decides to draw 3. - sin a house on a rectangular plot, so she decides to make the plan of the plot first. She map to a scale of 1: 50,000, of arectangular plot of land ABCD. The plot has the following AB = 6 cm; BC =8 cm and all angles are right angles. Estimate: 2. Tina wants to dimensions. + 1 + theadjoining diagram, in chords km. in Sq. km. (3) CDare AB,BC and equal. O is the centre of the LABC = 120 , Calculate: i) ZBAC circle. (4) If E ZBEC ii) ii) BED iv) ZCOD ,9) Solve the following. Mr. Chaturvedi has a recurring deposit account in Grindlay's Bank for 4 years at 11% p.a. (simple interest). he gets Rs. 101418.75 at the time of maturity, estimate the monthly instalment of Mr. Chaturvedi. (3) If 100 m on a bank of a above a river. river, At the Tanay observes angle of elevation of the cloud 3. The following figure hemisphere height of at represents is cloud at an angle of elevation of 30 ,which on a tree sitting 25 . Predict the width of the a solid one endanda cone the cylinder and a stationary same time, Sudesh at consisting of a right the other. Their cone are each of river, circular common 4 cm.Find the 20 m high, on the opposite is bank finds the correct to the nearest metre. (3) cylinderwith a radius is volume of the 7 cm. The solid. |4 Standing cm (4) 4 cm cm Q.10] Solve the following. 1 Given 2 Each x + 12x 6x2+ 8 of the 3. adisc is drawn at one of the Using ruler first last 9 letters 9 letters and compass of the in only, i) Construct a circumcircle of i) a is dividendo findx (3) :y. written on identicalcircular discs and put in random from the bag,what is the probability that the a bag. They are letter is: a vowel i) one of the i) If componendo and of the word 'AUTHORIZES' letters wellshuffled. i) y'+ 27y Using 9y2+ 27 Construct acyclic the alphabet which appears English alphabet which appears English construct a AABC such LABC ABCD, Such quadrilateral that that BC D is 6 in in = 5 cm the given word (3) a given word? and equidistant from AB = 6.5 cm AB and BC. and ABC = 120 (4)
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